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Introduction

Io stimo piú il trovar un vero, benché di cosa leggiera, che’l disputar lungamente delle massime questioni senza conseguir veritá nissuna. G. Galilei

Polymers are ubiquitous in Nature. They consist of a collection of many simple units (from the Greek word for “many” poly and for “unit” mer) and because of this, they are among the most simple examples of physical cooperativity. Polymers are made of repetitive patterns which make them easy to design, while their length can reach the million of units. Polymers can be thought of as very early examples of self-replicating objects: Given a single unit (a monomer) and enough substrate to form more units, a long sequence of monomers is bound to appear and eventually this can even break up forming many copies of itself. Nature has exploited this self-replicating ability by giving polymers a central role in Biology. Examples of biopolymers, or polymers produced by living organisms, are virtually endless: polysaccharides such as cellulose, starch and glycogen and, in general, carbohydrates are polymers made of repeating units which originate from the chemical group of monosaccharides such as glucose and are used as energy storage in mammals or scaffolding in plants. Filaments made of actin are polymers made up of proteins which, acting in concert with myosin, allow muscles to contract and extend. Microtubules are hollow and chiral polymers found throughout the cytoplasm formed as a long and dynamic self-assembly of tubulin which are crucial for intracellular transport and mitosis. Finally, possibly the most famous biopolymer in Nature is the deoxyribonucleic acid, or DNA, which is made as a collection of four nucleotides. I prefer finding something true, although of small importance, rather than keep debating on the major issues failing to achieve any truth. © Springer International Publishing Switzerland 2016 D. Michieletto, Topological Interactions in Ring Polymers, Springer Theses, DOI 10.1007/978-3-319-41042-5_1

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1 Introduction

DNA is an unparalleled example of polymers ability to self-replicate and to store information (Hurst and Dawkins 1992; Alberts et al. 2014). The self-replicating property of polymers is one of the many features which are fascinating about them. Ancient mesoamericans had already harnessed one of their other crucial properties. They discovered that the liquid sap extracted from the hevea tree would become elastic and resist tension once dried. From a microscopic point of view, they were witnessing the first instances of vulcanisation, which is nowadays widely used to make, among other things, shoes and tyres. The process for which cross-linking a polymeric liquid would confer elastic properties to it would have been fully understood only 3500 years later, around 1850 (Hosler et al. 1999). Another pivotal feature of polymers is that some of them are easy to design and cheap to synthesise. As a consequence, their artificial realisation soon started to attract economic interest. During the Second World War the production of synthe